New fuzzy numbers comparison operators in energy effectiveness simulation and modeling systems

Energy efficiency is often a key optimization problem. Many control systems use fuzzy logic and as a result applying compare operators to fuzzy numbers. The article deals with the issue of comparing fuzzy numbers. The similarity relation is most probably the most frequently used and the most difficult to precisely determine the convergence measure. Analysis of the similarity of two objects is a basic assessment tool and constitutes the basis for reasoning by analogy. It also directly affects the energy effectiveness of the universe that it controls. This article presents the methods for determining the similarity used in fuzzy logic. Many of these methods were dedicated only to fuzzy triangular or trapezoidal numbers (Dobrosielski et al. 2017, Chi-Tsuen Yeh 2017, Abbasbandy and Hajjar 2009). This was a computational inconvenience and posed a question about the axiological basis of this type of comparison. The authors proposed two new approaches for comparing fuzzy numbers using one of the known extensions of fuzzy numbers (Kacprzyk and Wilbik 2009, 2005). This allowed to simplify the operation and eliminate the duality (Zadrozny, 2004).